A Characterization of Mixed Unit Interval Graphs

We give a complete characterization of mixed unit interval graphs, the intersection graphs of closed, open, and half-open unit intervals of the real line. This is a proper superclass of the well known unit interval graphs. Our result solves a problem posed by Dourado, Le, Protti, Rautenbach and Szwarcfiter (Mixed unit interval graphs, Discrete Math. 312, 3357-3363 (2012)).Comment: 17 pages, referees' comments adde

Minimal Obstructions for Partial Representations of Interval Graphs

Interval graphs are intersection graphs of closed intervals. A generalization of recognition called partial representation extension was introduced recently. The input gives an interval graph with a partial representation specifying some pre-drawn intervals. We ask whether the remaining intervals can be added to create an extending representation. Two linear-time algorithms are known for solving this problem. In this paper, we characterize the minimal obstructions which make partial representations non-extendible. This generalizes Lekkerkerker and Boland's characterization of the minimal forbidden induced subgraphs of interval graphs. Each minimal obstruction consists of a forbidden induced subgraph together with at most four pre-drawn intervals. A Helly-type result follows: A partial representation is extendible if and only if every quadruple of pre-drawn intervals is extendible by itself. Our characterization leads to a linear-time certifying algorithm for partial representation extension

Unit Interval Editing is Fixed-Parameter Tractable

Given a graph~$G$ and integers $k_1$, $k_2$, and~$k_3$, the unit interval editing problem asks whether $G$ can be transformed into a unit interval graph by at most $k_1$ vertex deletions, $k_2$ edge deletions, and $k_3$ edge additions. We give an algorithm solving this problem in time $2^{O(k\log k)}\cdot (n+m)$, where $k := k_1 + k_2 + k_3$, and $n, m$ denote respectively the numbers of vertices and edges of $G$. Therefore, it is fixed-parameter tractable parameterized by the total number of allowed operations. Our algorithm implies the fixed-parameter tractability of the unit interval edge deletion problem, for which we also present a more efficient algorithm running in time $O(4^k \cdot (n + m))$. Another result is an $O(6^k \cdot (n + m))$-time algorithm for the unit interval vertex deletion problem, significantly improving the algorithm of van 't Hof and Villanger, which runs in time $O(6^k \cdot n^6)$.Comment: An extended abstract of this paper has appeared in the proceedings of ICALP 2015. Update: The proof of Lemma 4.2 has been completely rewritten; an appendix is provided for a brief overview of related graph classe

Boxicity and separation dimension

A family $\mathcal{F}$ of permutations of the vertices of a hypergraph $H$ is called 'pairwise suitable' for $H$ if, for every pair of disjoint edges in $H$, there exists a permutation in $\mathcal{F}$ in which all the vertices in one edge precede those in the other. The cardinality of a smallest such family of permutations for $H$ is called the 'separation dimension' of $H$ and is denoted by $\pi(H)$. Equivalently, $\pi(H)$ is the smallest natural number $k$ so that the vertices of $H$ can be embedded in $\mathbb{R}^k$ such that any two disjoint edges of $H$ can be separated by a hyperplane normal to one of the axes. We show that the separation dimension of a hypergraph $H$ is equal to the 'boxicity' of the line graph of $H$. This connection helps us in borrowing results and techniques from the extensive literature on boxicity to study the concept of separation dimension.Comment: This is the full version of a paper by the same name submitted to WG-2014. Some results proved in this paper are also present in arXiv:1212.6756. arXiv admin note: substantial text overlap with arXiv:1212.675

Structural parameterizations for boxicity

The boxicity of a graph $G$ is the least integer $d$ such that $G$ has an intersection model of axis-aligned $d$-dimensional boxes. Boxicity, the problem of deciding whether a given graph $G$ has boxicity at most $d$, is NP-complete for every fixed $d \ge 2$. We show that boxicity is fixed-parameter tractable when parameterized by the cluster vertex deletion number of the input graph. This generalizes the result of Adiga et al., that boxicity is fixed-parameter tractable in the vertex cover number. Moreover, we show that boxicity admits an additive $1$-approximation when parameterized by the pathwidth of the input graph. Finally, we provide evidence in favor of a conjecture of Adiga et al. that boxicity remains NP-complete when parameterized by the treewidth.Comment: 19 page

Box representations of embedded graphs

A $d$-box is the cartesian product of $d$ intervals of $\mathbb{R}$ and a $d$-box representation of a graph $G$ is a representation of $G$ as the intersection graph of a set of $d$-boxes in $\mathbb{R}^d$. It was proved by Thomassen in 1986 that every planar graph has a 3-box representation. In this paper we prove that every graph embedded in a fixed orientable surface, without short non-contractible cycles, has a 5-box representation. This directly implies that there is a function $f$, such that in every graph of genus $g$, a set of at most $f(g)$ vertices can be removed so that the resulting graph has a 5-box representation. We show that such a function $f$ can be made linear in $g$. Finally, we prove that for any proper minor-closed class $\mathcal{F}$, there is a constant $c(\mathcal{F})$ such that every graph of $\mathcal{F}$ without cycles of length less than $c(\mathcal{F})$ has a 3-box representation, which is best possible.Comment: 16 pages, 6 figures - revised versio

Stress induced polarization of immune-neuroendocrine phenotypes in Gallus gallus

Immune-neuroendocrine phenotypes (INPs) stand for population subgroups differing in immune-neuroendocrine interactions. While mammalian INPs have been characterized thoroughly in rats and humans, avian INPs were only recently described in Coturnix coturnix (quail). To assess the scope of this biological phenomenon, herein we characterized INPs in Gallus gallus (a domestic hen strain submitted to a very long history of strong selective breeding pressure) and evaluated whether a social chronic stress challenge modulates the individuals’ interplay affecting the INP subsets and distribution. Evaluating plasmatic basal corticosterone, interferon-γ and interleukin-4 concentrations, innate/acquired leukocyte ratio, PHA-P skin-swelling and induced antibody responses, two opposite INP profiles were found: LEWIS-like (15% of the population) and FISCHER-like (16%) hens. After chronic stress, an increment of about 12% in each polarized INP frequency was found at expenses of a reduction in the number of birds with intermediate responses. Results show that polarized INPs are also a phenomenon occurring in hens. The observed inter-individual variation suggest that, even after a considerable selection process, the population is still well prepared to deal with a variety of immune-neuroendocrine challenges. Stress promoted disruptive effects, leading to a more balanced INPs distribution, which represents a new substrate for challenging situations.Fil: Nazar, Franco Nicolas. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Investigaciones Biológicas y Tecnológicas. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas, Físicas y Naturales. Instituto de Investigaciones Biológicas y Tecnológicas; ArgentinaFil: Estevez, Inma. Centro de Investigación. Neiker - Tecnalia; EspañaFil: Correa, Silvia Graciela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigaciones en Bioquímica Clínica e Inmunología; ArgentinaFil: Marin, Raul Hector. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Investigaciones Biológicas y Tecnológicas. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas, Físicas y Naturales. Instituto de Investigaciones Biológicas y Tecnológicas; Argentin

The emergence of international food safety standards and guidelines: understanding the current landscape through a historical approach

Following the Second World War, the Food and Agriculture Organization (FAO) and the World Health Organization (WHO) teamed up to construct an International Codex Alimentarius (or 'food code') which emerged in 1963. The Codex Committee on Food Hygiene (CCFH) was charged with the task of developing microbial hygiene standards, although it found itself embroiled in debate with the WHO over the nature these standards should take. The WHO was increasingly relying upon the input of biometricians and especially the International Commission on Microbial Specifications for Foods (ICMSF) which had developed statistical sampling plans for determining the microbial counts in the final end products. The CCFH, however, was initially more focused on a qualitative approach which looked at the entire food production system and developed codes of practice as well as more descriptive end-product specifications which the WHO argued were 'not scientifically correct'. Drawing upon historical archival material (correspondence and reports) from the WHO and FAO, this article examines this debate over microbial hygiene standards and suggests that there are many lessons from history which could shed light upon current debates and efforts in international food safety management systems and approaches

The success-index: an alternative approach to the h-index for evaluating an individual's research output

Among the most recent bibliometric indicators for normalizing the differences among fields of science in terms of citation behaviour, Kosmulski (J Informetr 5(3):481-485, 2011) proposed the NSP (number of successful paper) index. According to the authors, NSP deserves much attention for its great simplicity and immediate meaning— equivalent to those of the h-index—while it has the disadvantage of being prone to manipulation and not very efficient in terms of statistical significance. In the first part of the paper, we introduce the success-index, aimed at reducing the NSP-index's limitations, although requiring more computing effort. Next, we present a detailed analysis of the success-index from the point of view of its operational properties and a comparison with the h-index's ones. Particularly interesting is the examination of the success-index scale of measurement, which is much richer than the h-index's. This makes success-index much more versatile for different types of analysis—e.g., (cross-field) comparisons of the scientific output of (1) individual researchers, (2) researchers with different seniority, (3) research institutions of different size, (4) scientific journals, etc

Challenges of Profile Likelihood Evaluation in Multi-Dimensional SUSY Scans

Statistical inference of the fundamental parameters of supersymmetric theories is a challenging and active endeavor. Several sophisticated algorithms have been employed to this end. While Markov-Chain Monte Carlo (MCMC) and nested sampling techniques are geared towards Bayesian inference, they have also been used to estimate frequentist confidence intervals based on the profile likelihood ratio. We investigate the performance and appropriate configuration of MultiNest, a nested sampling based algorithm, when used for profile likelihood-based analyses both on toy models and on the parameter space of the Constrained MSSM. We find that while the standard configuration is appropriate for an accurate reconstruction of the Bayesian posterior, the profile likelihood is poorly approximated. We identify a more appropriate MultiNest configuration for profile likelihood analyses, which gives an excellent exploration of the profile likelihood (albeit at a larger computational cost), including the identification of the global maximum likelihood value. We conclude that with the appropriate configuration MultiNest is a suitable tool for profile likelihood studies, indicating previous claims to the contrary are not well founded.Comment: 21 pages, 9 figures, 1 table; minor changes following referee report. Matches version accepted by JHE